Question

On a certain dry sunny day, a swimming pool's temperature would rise by 1.90°C if not for evaporation. What fraction of the water must evaporate to carry away precisely enough heat to keep the temperature constant?

Answer 1

Note :- Latent heat transfer occurs when mass of water evaporates from moist land surface or open water , moving heat from surface water to atmosphere , we need to find out fraction change in substance of water

Given data :

Let assume ;

Latent heat of vapourisation(Lv) = 2256 KJ /Kg or 2256 × 1000 J/kg

Specific heat of water (C)= 4186J/kg

Change in temperature (∆T) = 1.90 °C

​​​​​​heat energy absorbed by substance (Q)

Q= CM∆T --equation (1)

where M = Total mass of the water before vaporisation

Q = m*Lv -- equation (2)

​​​​​where m = mass of water after vaporisation

Equating (1) and (2) equations ; we get as

M*C*∆T = m*Lv

Substitute all values in above equation

m/M = (C*∆T)/ Lv

m/M = (4186×1.90)/ (2256×1000)

m/M = 0.00352

percentage change in fraction of Mass of water after change in vapourisation enough heat maintain temp constant is % m /M = 0.00352 ×100 = 0.352 %